The phenomenon of parametric amplification, such as occurs in a child's swing, has been studied since the early 19th century and occurs in oscillating systems in which a parameter (e.g., resonance frequency, spring constant, degree of dissipation, etc.) is modulated at a sub-multiple of twice the resonance frequency, 2ω0/n, to produce amplification in the response of the system. Parametric amplifiers have generated sustained interest because their operational noise can approach the quantum-limit and several implementations of this phenomenon have been demonstrated in electronic systems using varactors and Josephson junctions, optical systems using nonlinear materials, and in electromechanical systems.